英文标题：
《Fatou Property, representations, and extensions of law-invariant risk
measures on general Orlicz spaces》
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作者：
Niushan Gao, Denny H. Leung, Cosimo Munari, Foivos Xanthos
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最新提交年份：
2017
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英文摘要：
We provide a variety of results for (quasi)convex, law-invariant functionals defined on a general Orlicz space, which extend well-known results in the setting of bounded random variables. First, we show that Delbaen\'s representation of convex functionals with the Fatou property, which fails in a general Orlicz space, can be always achieved under the assumption of law-invariance. Second, we identify the range of Orlicz spaces where the characterization of the Fatou property in terms of norm lower semicontinuity by Jouini, Schachermayer and Touzi continues to hold. Third, we extend Kusuoka\'s representation to a general Orlicz space. Finally, we prove a version of the extension result by Filipovi\\\'{c} and Svindland by replacing norm lower semicontinuity with the (generally non-equivalent) Fatou property. Our results have natural applications to the theory of risk measures.
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中文摘要：
我们提供了在一般Orlicz空间上定义的（准）凸、定律不变泛函的各种结果，这些结果推广了有界随机变量设置中的著名结果。首先，我们证明了在一般Orlicz空间中失效的具有Fatou性质的凸泛函的Delbaen表示在定律不变性的假设下总是可以实现的。其次，我们确定了Orlicz空间的范围，其中Jouini、Schachermayer和Touzi关于Fatou性质的范数下半连续性的刻画仍然成立。第三，我们将Kusuoka表示推广到一般的Orlicz空间。最后，我们证明了Filipovi \\{c}和Svindland通过用（通常不等价的）Fatou性质替换范数下半连续性得到的扩展结果的一个版本。我们的结果自然适用于风险度量理论。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Risk Management 风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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